Papers

Hybrid quantum-classical compilation relates ideal operations and measurement outcomes to control pulses and device instructions. Existing formats each describe part of this process, and their preservation checks are often specific to one tool rather than to a common intermediate representation (IR). I present Qaiji-IR, an eight-layer IR family organized by a five-axis semantic contract for data, semantics, lowering, runtime, and verification. Its implementation provides typed circuits, an operation-semantics layer (L4) that records operation structure and checks a bounded set of equivalence rules, and a native-scheduling layer (L2) with separate validation. Nine circuit pairs are compared with ideal reference calculations. An aggregate baseline, which compares operation categories and measurement counts, accepts four behavior-changing transformations: gate reordering and changes of rotation angle, operand, or measurement destination. The L4 checker passes none of them. It distinguishes strict equality from equality up to global phase and returns unsupported when its rules cannot decide, as for valid rotation fusion. L2 validation checks native schedules against their source circuits, decomposition rules, local matrices, and configured timing. A single-qubit active-reset program is compiled through the Qaiji-IR frontend, a syntax adapter, and the EmuPlat backend into pulses and device instructions for a virtual pulse processing unit (VPPU). Injected binary outcomes select the conditional drive. Backend predicate tests reveal incorrect execution for equality to zero and for a nonbinary feedback value. This backend path does not use the validated L2 schedule. Physical measurement feedback, calibrated pulse fidelity, and feedback latency require further work.

In this paper we introduce and explore the following new graph invariant: For a graph $G$ on $k$ vertices, $G \neq K_k$, let $st(n,G)$ denote the maximum number of edges in a graph of order $n$ which does not contain any subgraph on $k$ vertices strictly containing $G$. A basic relation to classical Turán numbers is developed via the following: For $G$ on $k$ vertices, let $D(G) = \{ H : |H| = |G|, H = G + e \}$. Using this notion we prove that $ex(n,G) \leq st(n,G) = ex(n, D(G) ) \leq \min \{ ex(n,H) : H \in D(G) \}$ holds for all $n \geq |G|$. The family $D(G)$ happened to be smoothly amenable to the use of classical extremal results, and in many cases allows us to get asymptotically sharp estimates as well as exact values of $st(n,G)$. From the many results proved here we state the following as an illustration. (1) If $\chi(G) \geq 3$ and $\chi(D(G)) = \chi(G)$, then $st(n,G) = (1+o(1))ex(n,K_{\chi(G)})$. (2) If $\chi(D(G)) = \chi(G) +1$, then $G$ is a complete $\chi(G)$-partite graph and $st(n,G) = ex(n,K_{\chi(G) +1})$ for $n$ sufficiently large. (3) For $k$ odd, $k\geq 5$, $st(n,C_k) = ex(n,C_k) = ex(n,K_3)$ for $n$ sufficiently large. (4) If $T$ is a tree of order $q$ with diameter $k \geq 2$ and $q \geq k+1 \geq 3$, then $ex(n, \{C_3,...,C_{k+1}\}) \leq st(n,T) \leq ex(n, \{C_3,...,C_{k+1}\}) + (q-1)n$. Many results concerning even cycles, theta graphs, dense bipartite graphs and graphs of the form $G = G^* \cup tK_1$ are obtained, moreover the value of $st(n,G)$ is computed for all graphs on at most 4 vertices.

We investigate the cosmological implications of a power-law $f(Q, B)$ gravity model, where $Q$ denotes the non-metricity scalar and $B$ is the associated boundary term. We employ the Noether symmetry approach to identify the admissible functional form of the gravitational Lagrangian and to obtain the corresponding conserved quantities and exact cosmological solutions. Using the exact solution, we find that for this model parameter condition $\alpha+\beta>\frac{3}{2}$, the model exhibits the accelerating phase of the Universe. Furthermore, we have also discussed the model with recent observational data using a Bayesian Markov Chain Monte Carlo analysis. We consider different combinations of Cosmic Chronometers (CC), Pantheon+ & SH0ES, and DESI DR2 observations to constrain the model parameters and the Hubble constant $H_0$. The inferred value of $H_0$ depends on the adopted dataset combination, ranging from a higher value for the CC+Pantheon+ combination to a lower value for CC+DESI DR2, with the latter yielding $H_0=67.5^{+1.4}_{-1.6}\,\mathrm{km\,s^{-1}\, Mpc^{-1}}$, consistent with the Planck 2018 CMB-preferred value within the standard $\Lambda$CDM framework. The inferred \(H_0\) is strongly dataset dependent, spanning the range between the early-Universe and locally calibrated determinations. We further examine the posterior covariance and correlation matrices to identify parameter degeneracies and assess the robustness of the MCMC constraints. The background evolution also exhibits late-time accelerated expansion and remains compatible with the observational constraints. These results demonstrate that the $f(Q, B)$ model provides a viable alternative description of late-time cosmology.

Valiant and Vazirani isolate a satisfying assignment of a circuit with probability $\Omega(1/n)$. Dell, Kabanets, van Melkebeek, and Watanabe showed that success above $2/3$ implies $\mathrm{NP}\subseteq\mathrm{P/poly}$ and asked about the range in between. We show that every positive constant already implies the collapse: if a randomized nonuniform polynomial-size pruning procedure succeeds with probability $\epsilon$ on affine circuit inputs with at most $2^{\lfloor 2/\epsilon\rfloor}$ satisfying assignments, then $\mathrm{NP}\subseteq\mathrm{P/poly}$. Success $10/\log L$ on affine inputs with at most $L^{1/3}$ satisfying assignments suffices, where $L$ is the description length, and on inputs with one or two satisfying assignments the threshold $2/3$ drops to $3/5$. No cryptographic assumption is used, and the procedure may read the entire circuit. The proof compiles a pool of circuits into one circuit whose satisfying assignments are indexed by tags in $\mathbb{F}_2^d$. Each member is assigned an affine region of tag space, and if one member is unsatisfiable, the satisfying set shrinks to that member's region. Because regions may overlap and have different dimensions, the collapse reduces to a combinatorial bound: no set of tags meets more than a $2/d$ fraction of an equally weighted family of affine subspaces of all dimensions below $d$ in exactly one point. This regional counting cannot go below order $1/\log L$. The range between $\Theta(1/n)$, achieved by affine hashing, and $O(1/\log n)$ remains open.

Let $A\subset\mathbb{R}^d$, $d\geq3$, be the attractor of a self-similar IFS whose rotations generate a dense subgroup of $\mathrm{SO}(d)$. For every $1\leq k<\dim_{\mathrm{H}} A$ and $V\in\mathrm{Gr}(d,k)$, we prove that $\pi_VA$ has positive $k$-dimensional Lebesgue measure uniformly in $V$, and $\dim_{\mathrm{H}}(A\cap\pi_V^{-1}\{y\})=\dim_{\mathrm{H}} A-k$ for Lebesgue-almost every $y\in\pi_VA$. Moreover, if $\mu$ is a self-similar measure for such an IFS with $I_t(\mu)<\infty$ for some $k<t<d$, then every $\mu_V=(\pi_V)_*\mu$ is equivalent to the $k$-dimensional Lebesgue measure restricted to $\pi_VA$, with density $f_V$ satisfying $\sup_V\int_{\{f_V>M\}}f_V\,d\mathcal{L}_V^k\lesssim e^{-c(\log M)^{1/3}}$. Under strong separation, the conditional measures on the fibres are exact dimensional of dimension $\dim_{\mathrm{H}}\mu-k$. The proof uses self-similarity to iterate $L^1$ norms of differences of the Gaussian-smoothing of $\mu_V$ between scales. Unlike $L^q$, $q>1$, the $L^1$ norm does not grow under rescaling, allowing Varjú's $L^2$ weak gap theorem under dense support condition to be used, and avoiding to use the much stronger uniform spectral gap assumption.

True random number generation is a critical capability for fault-tolerant quantum computing at millikelvin temperatures. Yet existing Josephson-junction-based TRNGs all rest on a widely accepted but untested assumption: that reliable entropy extraction requires precisely controlled device parameters. Here we show that this assumption does not always hold. We demonstrate a counterintuitive finding: a single current-biased Josephson junction, regardless of its parameter quality, can serve as a cryptographic-grade true random number generator. To establish the universality of this conclusion, we deliberately selected the most extremely deviated devices from fabrication, with critical currents three orders of magnitude away from theoretical predictions and $I_cR$ products an order of magnitude above conventional values, as the ultimate stress test. Even under these extreme conditions, the raw Shannon entropy reaches 0.9981~bit (99.8% of the theoretical maximum), with a min-entropy of 0.9271~bit. Using a square-wave pulsed-bias scheme, we tune the switching probability to $P\approx0.5$. After SHA-256 post-processing, the bitstreams pass all 15 NIST SP 800-22 tests under a conservative $m=3$ criterion that is more demanding than the standard recommendation, and this certification holds across the entire 100-700~mK operating window of a dilution refrigerator.

Motivated by the study of asymptotics of quantum invariants, Dimofte and Garoufalidis introduced a power series associated to a suitable ideal triangulation of a cusped hyperbolic $3$-manifold. They proved that its constant term can be written in terms of Neumann-Zagier data and the complex shape parameters of ideal tetrahedra, and conjectured that it equals the adjoint twisted Reidemeister torsion. On the other hand, in the study of asymptotics of Turaev-Viro type invariants of cusped $ 3$-manifolds, the authors, together with Liu, Sun and Yang, found that the one-loop terms of their asymptotic expansions could be written in terms of Gram matrices and decorated edge lengths of ideal tetrahedra. In this paper, we prove the conjecture of Dimofte and Garoufalidis and relate the one-loop term appearing in the Turaev-Viro type invariant to the adjoint twisted Reidemeister torsion.

We prove that lambda_SSS >= 1.80220 for the smallest limiting trace-to-degree ratio of totally positive algebraic integers, improving the bound 1.80203 obtained by Orloski, Talebizadeh Sardari and Smith. The proof exhibits an explicit probability measure on [0,8] together with eighteen integer polynomials, and verifies their dual inequality on the whole of [0,infinity) by interval bisection. The certificate assumes nothing about the data it is built from: an error in that data can only weaken the bound, never invalidate it.

Gaussian processes (GPs) provide a flexible nonparametric framework for modeling time series through appropriately chosen kernel functions. This chapter introduces the basic formulation of Gaussian processes, commonly used kernels, GP regression, hyperparameter estimation, and model evaluation using in-sample and out-of-sample criteria. Applications to stationary, quasi-periodic, and seasonal time series illustrate how individual and composite kernels can represent different forms of temporal variation. Additive kernels also provide interpretable decompositions into latent components such as trend, smooth local variation, and seasonality, while product kernels allow more complex dependence structures to be constructed. Finally, Gaussian process state-space models (GP-SSMs) are briefly introduced, and a nonlinear example demonstrates how a GP transition model can be combined with particle filtering and smoothing for latent-state estimation.

Existing formal mathematics benchmarks, such as miniF2F, ProofNet, and PutnamBench, primarily evaluate models on constructing complete formal proofs for challenging problems. Because success is measured at the theorem level, these benchmarks offer limited insight into models' step-level formal reasoning. Evaluating this capability separately enables finer-grained diagnosis of model limitations than theorem-level evaluation alone. To fill this evaluation gap, we introduce ProofGap, a fine-grained benchmark for step-level formal reasoning. ProofGap is constructed through a natural-language proof-processing pipeline that decomposes each reasoning step into one or more aligned proof gaps. Applying this pipeline to natural-language solutions to 3,015 exercises in B. P. Demidovich's Problems in Mathematical Analysis yields 26,116 gaps. The benchmark focuses on mathematical analysis, a domain that remains challenging for current models. By supplying the local context and target explicitly, gap completion isolates local formal proof construction from end-to-end proof composition, enabling more precise localization of model failures. Natural-language solutions serve as the provenance of these obligations, while the benchmark task itself starts from an already formalized local context and goal. Beyond benchmarking, the same pipeline may support future proof-verification systems, provided that semantic translation and sequential proof composition are handled reliably.

This paper calculates the lepton flavor universality including the $b\rightarrow c\ell \nu$ process under the U(1) extension of the minimal supersymmetric standard model ($U(1)_X$SSM), and provides numerical analysis and summary. The numerical results are used to create one-dimensional and multi-dimensional plots to analyze the impacts of various parameters on the ratios $(\frac{R_{J/\psi}}{R^{SM}_{J/\psi}}$, $\frac{R_{{D}_s}}{R^{SM}_{D_s}}, \frac{R_{{D^*}_s}}{R^{SM}_{D^*_s}},\frac{R_{{\Lambda}_c}}{R^{SM}_{\Lambda_c}})$. The results show that several parameters have a certain effect on the ratios. Although it can't match the experimental data very well, with the right combination of parameter values, it can give better numerical results than the Standard Model. This shows that the $U(1)_X$SSM is very helpful for studying $b\rightarrow c\ell \nu$ processes.

The $k$ vertex-disjoint paths problem asks whether, given a graph $G$ and $k$ pairs of vertices $(s_1,t_1)$, \ldots, $(s_k,t_k)$, $G$ has $k$ pairwise vertex-disjoint paths connecting $s_i$ and $t_i$ for all $1\leq i\leq k$. If $G$ is undirected, then this problem is NP-complete, but there exist FPT algorithms parameterized by $k$.Since these algorithms involve an extremely large function on $k$, algorithms for restricted graphs have also been investigated. In particular, a $2^{2tw\log tw+O(tw)}\cdot n$ time algorithm for undirected graphs with $n$ vertices and treewidth $tw$ is proposed by Scheffler (Technical Report 396, TU Berlin, '94), and it is proved by Lokshtanov, Marx, and Saurabh (SIAM J. Comput. '18) that, under the ETH, there exists no $2^{o(pw\log pw)}\cdot n^{O(1)}$ time algorithm for either directed or undirected graphs with pathwidth $pw$ and for $k=\Omega(pw^4)$. It has not been known whether the lower bound also holds for a smaller $k$. In this paper, we prove that, for both the directed and undirected cases, there is an algorithm faster than Lokshtanov et al.'s lower bound for $k=tw^{o(1)}$ by proposing a $2^{O((tw+k)\log k)}\cdot n$ time algorithm. Besides, we prove a lower bound that, under the SETH, there exists no $(2-\epsilon)^{pw\log pw}\cdot n^{O(1)}$ time algorithm for directed graphs and for a general $k$. This lower bound is tight because, with slight modifications, Scheffler's algorithm runs in $2^{pw\log pw+O(pw)}\cdot n$ time also for directed graphs.

All objects illuminated with light inevitably cast a shadow – a universal phenomenon encapsulated in the fundamental property that all passive systems with plane-wave illumination feature a non-zero forward scattering amplitude. Since Kerker's landmark 1983 paper, considerable effort has been devoted to overcoming this limitation and achieving the elimination of forward scattering – an objective now widely known as the zero-forward Kerker scattering. However, this objective is fundamentally restricted to active systems, requiring either physical gain in materials or virtual gain in the excitation source. Despite advances in active materials science and non-Hermitian photonics, the experimental realization of zero-forward Kerker scattering still remains an open challenge. Here, we show, both theoretically and experimentally, how zero-forward Kerker scattering can be effectively synthesized by a weighted superposition of readily accessible real-frequency responses. Our synthetic recipe builds on creating an artificial pole at a complex frequency that prevails over inherent scattering poles. These findings not only unlock a realistic experimental framework for non-Hermitian light-matter interactions, but also hold technological relevance for non-invasive sensing and imaging.

In this work, we focus on photorealistic sign avatar modeling, which is crucial for effective communication with the Deaf community and is characterized by complex hand gestures and nuanced facial expressions. To this end, we introduce MVSign, the first multi-view Chinese sign language dataset co-designed with Deaf experts, featuring diverse gestures and rich annotations. For precise SMPL-X annotation, we develop a hybrid fitting pipeline that produces accurate body, hand, and facial parameters and can also be applied to the monocular setting. Building on MVSign, we propose a decoupled sign avatar representation that isolates body, head, and hand components to capture complex articulations, together with a motion-aware sampling strategy to handle motion blur and balance gesture diversity. Extensive experiments demonstrate that our method achieves high-fidelity visual results on MVSign, particularly in detailed hand and facial regions, and generalizes well to in-the-wild monocular sign language videos. Project page: https://naaapi.github.io/PHOSA.

We propose Sufficiently Reduced Distributional Regression (SRDR), a generative method that combines conditional distribution estimation with nonlinear sufficient dimension reduction (SDR). It builds on a characterization of sufficiency through strictly proper scoring rules: a dimension reduction is sufficient if and only if predicting the response from the reduced covariates incurs no loss in expected score relative to the full covariates. Sufficient dimension reduction thus becomes a risk minimization problem. SRDR jointly trains a dimension reduction map and a generative prediction model by minimizing the energy score, which can be estimated by sampling without density evaluation or adversarial training. The framework extends to multi-environment data and to classification. We prove that the estimated conditional distributions converge in energy distance to the true ones, which implies that the learned representation is asymptotically sufficient. In simulations and applications to CT slice localization, superconductivity, and digit classification, SRDR recovers low-dimensional sufficient structure and matches or outperforms state-of-the-art nonlinear SDR methods in representation quality and predictive performance.

To address the widespread sensitivity of surface-mounted permanent magnet synchronous motor (SPMSM) sensorless control to motor parameters, this paper proposes a temporal regression-based model-free sensorless control (TFC) method. First, voltage integrals and current increments over consecutive short intervals are stacked to construct a finite window regression, in which the unknown stator inductance appears as a common scalar coefficient. Second, a projection operator constructed from the stacked current increments eliminates the inductance term, and a least-squares formulation is developed to reconstruct the rotor flux vector. Meanwhile, the analysis of the projected regression and current-flux geometry establishes a two-dimensional direction vector whose components share a common amplitude containing the stator resistance and flux linkage. This amplitude cancels during position extraction. By setting the resistance reference to zero, the proposed method estimates the position without specifying the stator resistance, inductance, or flux linkage. Finally, experimental results verify the effectiveness of the proposed TFC method.

In this paper, we prove that any compact immersed disk in a half $3$-space that has constant anisotropic mean curvature and satisfies the anisotropic capillary boundary condition is a homothetic Wulff cap.

Let $\Omega\subset\mathbb{R}^N$ be a bounded convex domain, and let $A=-\Delta_D$ be the Dirichlet Laplacian. For every $s>0$ with $N>2s$, we prove that the Green-kernel transform $(x,y)\mapsto K_{s,\Omega}(x,y)^{-1/(N-2s)}$ extends continuously by zero to the diagonal and is jointly convex on $\Omega\times\Omega$. We prove that the regular part extends real analytically across the diagonal and that the associated Robin function is strictly convex and diverges to $+\infty$ at the boundary. Hence it has a unique critical point. If $\Omega$ is of class $C^{2,\vartheta}$, this point is nondegenerate for every $s>0$ with $N>2s$. Moreover, the Hessian of the Robin function is positive definite throughout $\Omega$ when $0<s<1$ or $N>3s$. The arguments combine convexity inequalities for Dirichlet heat kernels, a weighted boundary identity at fractional orders, and a finite-part transfer of Hessian positivity between spectral powers. In particular, the results apply to spectral fractional Dirichlet Laplacians and Navier polyharmonic operators.

Large audio-language models (LALMs) expand language models to process and interpret audio, but also expose them to heterogeneous audio jailbreaks. We ask whether successful jailbreaks reflect failures to recognize harmful intent or failures occurring after such recognition. Layer-wise probing reveals the latter: risk-related information remains decodable from intermediate representations, yet the internal risk signal fails to translate into refusal in later-layer processing. We identify this discrepancy as the risk-to-refusal gap. Building on this finding, we propose AEGIS, a detect-then-intervene defense whose mid-layer risk gate selectively activates downstream safety adapters. Across six LALMs and three heterogeneous audio jailbreak benchmarks, AEGIS reduces the average unsafe rate from 17.9% to 0.4%, while causing only a marginal increase in over-refusal on benign inputs. These results establish selective internal intervention as an effective path toward more robust refusal in LALMs. The code is available at https://github.com/azzzzliao/aegis-audio-defense.

We investigate the expected reconstruction risk of trigonometric polynomial models under different sampling schemes. Through numerical experiments, we observe that when the sampling nodes $\{t_l\}_{l=1}^m$ are i.i.d. random variables uniformly distributed over $[0,1)$, the associated structured random matrix $\pmb{A} \in \mathbb{C}^{m \times N}$ with $A_{l,k} = e^{2\pi \mathrm{i} kt_l}, k \in \Gamma = \{-q, \dots, q\}, N = 2q+1$ frequently becomes nearly singular or severely ill-conditioned. As a consequence, the expected reconstruction risk exhibits divergent behavior. In contrast, when the sampling nodes $t_l$ are either equidistant points or small random perturbations of an equidistant grid, the expected reconstruction risk undergoes a sharp phase transition at the interpolation threshold $m=N$. To better understand the underlying mechanisms behind these different phenomena, we characterize the expected reconstruction risk through the spectral quantity $\sum_{i=1}^{r} \frac{1}{\sigma_i^2(\pmb{A})}$, where $\sigma_i(\pmb{A})$ denotes the singular values of the sampling matrix. Based on this spectral representation, we theoretically prove that the expected reconstruction risk diverges under uniformly distributed random sampling. Furthermore, we derive an explicit formula for the expected reconstruction risk in the equidistant sampling case and establish upper and lower bounds for the expected reconstruction risk under jittered sampling.

We investigate a variant of the deep BSDE method introduced by E et al. (2017, 2018). The key novelty is that we establish an a-posteriori convergence result for the approximation of strongly coupled forward-backward stochastic differential equations (FBSDEs), i.e., our result holds without any assumptions on small time horizons, monotonicity or weak coupling that are typically imposed in the literature on the deep BSDE method. Instead, we rely on smoothness assumptions on the coefficients and cover FBSDEs in which the coupling of the BSDE into the SDE depends on both the backward component $Y$ and the control component $Z$. Numerical experiments illustrate the theoretical results and demonstrate the applicability of the proposed approach.

The interaction between conjugated molecules and intense electric field pulses drives a plethora of intriguing nonlinear phenomena, including optical limiting. While excited-state absorption was recently identified as the primary mechanism for this effect in thiophene oligomers, open questions remain regarding field-dependent population dynamics under intense laser driving. Using real-time time-dependent density functional theory combined with a determinant-overlap population framework, we track the intensity-dependent nonlinear response of a single thiophene ring (1T) and quaterthiophene (4T) as prototypical members of the oligothiophene family with different length and symmetry. We demonstrate that extended $\pi$-conjugation in 4T lowers nonlinear excitation thresholds by orders of magnitude compared to 1T. State-resolved population dynamics reveal complete ground-state depletion accompanied by sequential excited-state absorption channels under intense driving. High-harmonic generation spectra explicitly reflect molecular symmetry constraints, while energy-resolved occupation densities confirm continuous orbital redistribution across the $\pi^*$-manifold. This work provides dynamic physical insights for engineering organic materials with tailored nonlinear optical properties.

Visual software often needs a decision over supplied alternatives rather than a generated explanation. We present PixelJev, a native-image decision interface that maps an image, a task instruction, and a runtime candidate set to a structured choice and candidate-conditioned probabilities using small open multimodal models. Its initial realization unifies recognition and multiplechoice visual question answering through an existing language-model readout, with separately evaluated options for frozen inference, language-side adaptation, and held-out calibration. Across seven benchmark evaluations, 64-shot source adaptation raises Pets accuracy from 60.13% to 92.40% across optimization seeds and transfers to natural resampling, new texture labels, and A-OKVQA without target fitting, while frozen inference already supports both VQA tasks. A matched prompt-only follow-up on Pets and ScienceQA attributes the large Pets gain to adaptation and identifies a narrower output validity benefit of candidate readout in adapted VQA. Specialist DINOv2 probes remain stronger on source recognition, frozen 4B is stronger than adapted 2B on DTD and ScienceQA, and accuracy gains do not ensure calibrated target probabilities. These findings establish a working starting point for general-purpose visual decision models and identify the remaining requirements: schema robustness, cross-family transfer, and reliable use of visual evidence.

While graph-based and hypergraph-based Retrieval-Augmented Generation (RAG) significantly mitigate hallucinations in Large Language Models (LLMs), existing structure-based RAG systems typically adopt static traversal strategies regardless of the query complexity. We identify this “static retrieval fallacy” as a primary source of computational redundancy for simple queries and cognitive context gaps for complex reasoning tasks. To balance reasoning quality and inference efficiency, we propose Asymmetric Dynamic Routing (ADR), an intent-conditioned retrieval framework operating over hierarchical knowledge graphs. ADR employs a lightweight structured classifier to dynamically dispatch queries among three asymmetric topological traversal operators: localized fact anchoring, bottom-up adjacency diffusion, and top-down insight grounding, which collectively enable bidirectional information flow across hierarchical knowledge layers. Extensive empirical evaluations across five domain-specific corpora demonstrate that ADR maintains strong reasoning performance while reducing prompt token consumption by up to 48.7% and end-to-end query latency by 45.3%, yielding a favorable quality–efficiency trade-off for query-adaptive Hypergraph RAG.

Neural networks are typically adapted by computing gradients and updating model parameters. We investigate whether task-specific adaptation can instead emerge from a meta-learned self-organising process that requires no gradients at adaptation time. We instantiate this idea with a Neural Cellular Automaton in which locally interacting recurrent cells maintain both a recurrent state and a fast associative memory. During meta-training, backpropagation is used to learn the recurrent dynamics together with how the memory is read and written. Once training is complete, the slow model parameters remain fixed, and online adaptation occurs only through cellwise memory updates driven by local prediction errors and a delta rule. We evaluate whether the learned mechanism can adapt to semantically distinct held-out classification tasks. A single pass over the support data produces substantial improvements in held-out performance without gradient computation or parameter updates during adaptation, and the mechanism remains effective across large changes in the number of examples processed jointly. These results show that task-specific adaptation can be achieved through explicit fast-memory updates while keeping the slow model parameters fixed.

Periodic unsteady flows are common in forced-motion and fluid-structure interaction problems. Their parametric analysis typically requires repeated high-fidelity simulations, whereas existing reduced-order and surrogate models generally rely on pre-generated flow-field or aerodynamic data. This study proposes a purely physics-driven framework for solving parametric periodic flows and finite-amplitude aeroelastic responses. First, a Periodic Physics-Informed Neural Network (P-PINN) is developed to directly solve periodic flows by imposing temporal periodicity over a single motion cycle, thereby avoiding the need to resolve the long transient evolution preceding the establishment of the periodic state. The flow conditions and motion parameters are further incorporated as network inputs to construct continuous parametric representations of the periodic flow field and aerodynamic forces. On this basis, the parametric aerodynamic model is coupled with the structural dynamic equation through first-order harmonic balance to solve the response amplitude and frequency of a single-degree-of-freedom aeroelastic system. This framework is validated using forced-motion cases of a circular cylinder and an airfoil, demonstrating accurate reproduction of periodic aerodynamic forces, surface load distributions, and instantaneous flow fields under different flow and motion parameters compared with time-marching results. Furthermore, aeroelastic analysis is conducted for an elastically mounted circular cylinder at subcritical Reynolds numbers, and the resulting aeroelastic response agrees well with fully coupled CFD/CSD results. Once trained offline, the parametric model can be repeatedly evaluated for different structural parameter states, enabling the complete aeroelastic response curve to be obtained online within seconds, without repeated long-time fluid-structure interaction time marching.

A fundamental result due to Fonf (1981) asserts that the unit sphere of every polyhedral Banach space is covered by true faces of the unit ball. The principal aim of our paper is to study the validity of the same result for polyhedral normed spaces and present some applications. Our first main result is that if $X$ is a polyhedral normed space with property ($\Delta$), then its unit sphere is covered by algebraic true faces. It then follows that if the space is additionally (VI)-polyhedral, then its unit sphere is covered by genuine true faces. We also present several counterexamples showing that these results are optimal in a strong sense. For instance, we show that there exist (V)-polyhedral normed spaces whose unit ball doesn't have any algebraic true face at all, and that there exist polyhedral normed spaces with ($\Delta$) whose unit sphere is not covered by true faces. Further, we give an example of a polyhedral normed space such that the set of strongly exposed points of the unit ball is dense in the sphere, and some results and counterexamples concerning boundaries of polyhedral normed spaces. Our principal application of this material involves locally finite tilings of normed spaces, and we show that a normed space admits a locally finite tiling (by bounded convex bodies) if and only if it admits a (VI)-polyhedral norm with ($\Delta$). In particular, such a tiling exists in every polyhedral Banach space with ($\Delta$), which generalises a result of Fonf.

Chain-of-thought (CoT) instructions can distort multiple-choice VLM evaluation when a scorer appends a reasoning cue but reads answer-label logits before the model generates any rationale. We call this CoT-prefix scoring. On ScienceQA, Qwen2.5-VL-7B drops from 80.76% to 45.48%, and across five option-content permutations 93.54% of CoT-prefix predictions select the first slot. Condition-matched linear probes recover 78.94% from the same hidden states, while free generation restores 75.24%, showing that the answer often survives the prefix and the immediate readout fails. Vocabulary and layer diagnostics explain the mismatch: probability mass moves toward continuation tokens, while answer information remains linearly accessible in late layers. The effect recurs with varying severity across datasets and models, though not universally. These results show that CoT-prefix scoring can confound model knowledge with an evaluation-interface mismatch and should be avoided unless the requested and scored output events are aligned.

Discharge ignition events in dielectric barrier discharges (DBDs) self-organise into spatio-temporal patterns with varying degrees of order. The complex dynamics of a DBD and intricate structure of occurring patterns complicate the formulation of predictive, mechanistic descriptions. We present the formulation of a reduced-order model that describes the re-ignition dynamics between consecutive discharges appearing at the same position inside a DBD arrangement. The model is derived from an equivalent electric circuit and validated against fluid-Poisson simulations and experiments performed with a multi-filament arrangement in air-like gas mixtures at atmospheric pressure driven by sinusoidal high-voltage waveforms. The experimental scenarios include a highly ordered regime where discharges ignite at regular time and space intervals generating a pattern stable over several periods, and an unstable regime with discharges appearing at seemingly random positions and times. The model accuracy is assessed in both regimes and it is found that the associated prediction uncertainty provides a quantitative measure of the spatial order of the discharge pattern.

Lexical borrowings are words from one language that are introduced into another language. Identifying lexical borrowings in text is a relevant task for data-centric fields in Linguistics such as lexicography or corpus linguistics, but none of the standard libraries for text processing offers such a functionality. In this paper we present pylazaro, an open-source Python package for the automatic extraction of unassimilated lexical borrowings (mostly anglicisms) from Spanish text. pylazaro offers a single interface to five sequence labeling models that were trained using different libraries, so that users can run and switch between them without having to deal with the idiosyncrasies of each library. We describe the design and usage of the package, contrast the performance of its models with that of general-purpose LLMs (which perform poorly at this task: F1 below 0.40, compared to 0.86 for the best model in pylazaro) and report on its adoption: pylazaro has been downloaded more than 58,000 times and is the library behind Observatorio Lazaro, a resource that monitors anglicism usage in the Spanish press. pylazaro can be installed via PyPI, is documented in readthedocs and can be tried through a live demo hosted on HuggingFace Spaces.